Question

Point (x,0) is equidistant from the points (7,6) and
(9, 4). What is the value of x?​

Answer 1

3

Step-by-step explanation:

Let A(x,0), B(7,6), C(9,4)

therefore, AB =AC

from Distance Formula,

$\sqrt{(7 - x) {}^{2} + (6 - 0) {}^{2} } = \sqrt{(9 - x) {}^{2} + (4 - 0) {}^{2} } \: \:$

so, 7²-2.7.x+x²+6² = 9²-2.9.x+x²+4²

or, 49-14x+x²+36=81-18x+x²+16

(x² gets cancelled)

or, 85-14x=97-18x

or, 85-97=-18x+14x

or, -12=-4x

or, X = 3